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CUET · MATHS · PYQ PAPER 2023

The differential equation representing family of circles with centre at point (4, 0) is:

  1. A \(\frac{d y}{d x}=\frac{4-x}{y}\)
  2. B \(\frac{d y}{d x}=\frac{y}{4-x}\)
  3. C \(\frac{d y}{d x}=\frac{4+x}{y}\)
  4. D \(\frac{d y}{d x}=\frac{y}{4+x}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{d y}{d x}=\frac{4-x}{y}\)

Step-by-step Solution

Detailed explanation

Equation of circle: \((x-4)^2 + y^2 = r^2\) Differentiate: \(2(x-4) + 2y \frac{dy}{dx} = 0\) Simplify: \((x-4) + y \frac{dy}{dx} = 0\) Solve for \(\frac{dy}{dx}\): \(y \frac{dy}{dx} = -(x-4)\) Result: \(\frac{dy}{dx} = \frac{4-x}{y}\)